By starting with Abraham, Matthew points to the purpose for the establishment of Israel: to carry forward the seed of the woman to Christ. Calling Jesus the son of Abraham
also shows that the promises to Israel, first given to Abraham (Genesis 12:3), were fulfilled in Christ. Jesus is also called the son of David (Psalm 110:1, quoted in Matthew 22:44), because he fulfills the messianic promises given to David.
As a Son of Abraham’s descendant David, Jesus is also a Son of Abraham. David is specifically mentioned here not only because in his role of king he foreshadowed the Messiah, but also because he was the last man in the genealogical line to whom it was revealed that the Messiah would be one of his own descendants. Abraham is mentioned because he was the first in the line of the Messiah’s ancestors to be set apart for the purpose of producing the holy seed, of which he had repeatedly received the promise. Matthew does not trace the genealogy back to Israel’s prehistory like Luke does, but specifically strives to show how the promises to Israel were fulfilled in Christ. Israel existed for Christ’s sake, and Christ is the great Son of David (see Psalm 110:1, quoted in Matthew 22:44), and Abraham’s promised seed (Genesis 12:3). Therefore, his genealogy begins with Abraham.1
1 The book of the genealogy of Jesus Christ, the son of David, the son of Abraham.